Class time using rounding and compensating to solve addition problems
Class time solving multiplication word problems
Class time using multiplication bracket notation
- This exemplar homework sheet is designed to extend the work done in class, not simply repeat it. As such large numbers of carefully graded questions that slowly increase in difficulty are not required.
- Students are being encouraged to think more, rather than simply follow algorithms, so the sheet should encourage independent thought and action.
Comments on the Exercises
Word problems – many students find word problems difficult, and these form the core of many NCEA assessments. Consequently practice with them is continually needed. Here the focus is also on setting out and explaining what is being done at each step, as this is also a maths based skill required for NCEA. This could have been the focus of a lesson at some stage in the past, then simply be part of the regular homework – or it may be a way of starting the next lesson where this aspect of mathematics is the teaching point for the day.
The word problems follow a format that is common in NCEA achievement standards assessment – with a bit more scaffolding. It requires students to explain what they are calculating at each step.
Question 4 could be used to prove students have actually done their homework – and good questions are a source of further worksheets for next year.
Rounding and compensating. This exercise revises a strategy and when it works – but over both domains rather than within a single domain. Be aware that this particular strategy works for +/-/?, but not division. (A very good extension problem is to ask students why it does not…) Getting students to look at decimals may be revision for some – or it may be an extension piece that is making student really think. In either case, the focus is on explanation rather than simple computation. This also means that question 13 is an extension problem that may not be used with all students.
The decimal problems should be collected and marked, if this is set, as it may bring to light a number of understanding issues around both decimals and the strategy
Multiplication without the sign – introduces a small piece of knowledge that would otherwise take lesson time. It is also serving as part of the bridge from number to algebra and the development of the distributive law. One concern with this exercise is that it has only a few problems to support new learning, so may need follow up in group time.
The exercise can be followed up by using the notation in this format in group teaching sessions.
Notes on marking homework
Checks that homework has been completed can be run very quickly at the start of the period, while someone is running the starter.
- Actual marking for a lot of numeracy homework could be done by students using a calculator at the start of independent work time. Alternatively, the answer sheet could be made available at the start of independent work time, with students self-marking this way. In other words it can be part of students’ responsibilities so does not have to be a teacher responsibility.
- Handing in word questions is a good way of developing a bank of student-centred practical contexts for word problems. It is also a way of quickly monitoring that students are actually doing their homework and making sense of it without too much marking.
- With wall displays and project work, students can be given the task of marking (or peer reviewing) work. This not only removes the need for the teacher to mark, but also gives students a clearer idea of what quality work looks like, and how it is identified.
Free Math Worksheets for Grade 6
This is a comprehensive collection of free printable math worksheets for sixth grade, organized by topics such as multiplication, division, exponents, place value, algebraic thinking, decimals, measurement units, ratio, percent, prime factorization, GCF, LCM, fractions, integers, and geometry. They are randomly generated, printable from your browser, and include the answer key. The worksheets support any grade 6 math program, but have been specifically designed to match Math Mammoth grade 6 curriculum.
The worksheets are randomly generated each time you click on the links below. You can also get a new, different one just by refreshing the page in your browser (press F5).
You can print them directly from your browser window, but first check how it looks like in the "Print Preview". If the worksheet does not fit the page, adjust the margins, header, and footer in the Page Setup settings of your browser. Another option is to adjust the "scale" to 95% or 90% in the Print Preview. Some browsers and printers have "Print to fit" option, which will automatically scale the worksheet to fit the printable area.
All worksheets come with an answer key placed on the 2nd page of the file.
In sixth grade, students will start the study of beginning algebra (order of operations, expressions, and equations). They learn about ratios & percent and start using integers. Students also review long division, factoring, fraction arithmetic, and decimal arithmetic.In geometry, the focus is on the area of triangles and polygons and the volume of rectangular prisms. Other topics include rounding, exponents, GCF, LCM, and measuring units. Please note that these free worksheets do not cover all 6th grade topics; most notably, they do not include problem solving.
Multiplication and Division and Some Review
- 1-digit divisor, 5-digit dividend, no remainder
- 1-digit divisor, 5-digit dividend, with remainder
- 1-digit divisor, 6-digit dividend, no remainder
- 1-digit divisor, 6-digit dividend, with remainder
- 1-digit divisor, 7-digit dividend, no remainder
- 1-digit divisor, 7-digit dividend, with remainder
- 2-digit divisor, 5-digit dividend, no remainder
- 2-digit divisor, 5-digit dividend, with remainder
- 2-digit divisor, 6-digit dividend, no remainder
- 2-digit divisor, 6-digit dividend, with remainder
- 2-digit divisor, 7-digit dividend, no remainder
- 2-digit divisor, 7-digit dividend, with remainder
- 3-digit divisor, 6-digit dividend, no remainder
- 3-digit divisor, 6-digit dividend, with remainder
- 3-digit divisor, 7-digit dividend, no remainder
- 3-digit divisor, 7-digit dividend, with remainder
- Multiply decimals, writing the numbers under each other (0-2 decimal digits)
- Divide a whole number or a decimal by a whole number, need to add zeros to the dividend
- Convert a fraction to a decimal using long division, rounding the answers to three decimals
Convert measuring units using long division & multiplication
Primary Grade Challenge Math by Edward Zaccaro
A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.
Order of operations
- Three operations, uses ÷ for division, no exponents
- Four operations, uses ÷ for division, no exponents
- Two or three operations, uses the fraction line for division, no exponents
- Two or three operations, uses the fraction line for division, exponents included
- Two, three, or four operations, uses the fraction line, exponents included
Key to Algebra Workbooks
Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.
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Fractions vs. Decimals
- Decimals to fractions or mixed numbers (tenths/hundredths/thousandths)
- Decimals to fractions or mixed numbers (up to millionths)
- Mixed numbers to decimals (denominators 10, 100, and 1000)
- Proper and improper fractions to decimals (denominators 10, 100, or 1000)
- Proper fractions to decimals (denominators powers of ten till 1,000,000)
- Mixed numbers to decimals (denominators powers of ten, till 1,000,000)
- Fractions or mixed numbers to decimals (easy, varied denominators)
- Fraction to decimals - need long division
- Fractions to decimals - mixed practice
Decimal Addition and Subtraction
Key to Decimals Workbooks
This is a workbook series by Key Curriculum Press that begins with basic concepts and operations on decimals. Then the books cover real-world uses of decimals in pricing, sports, metrics, calculators, and science.
The set includes books 1-4.
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Multiply in columns
- Easy decimal division (dividend has 1-2 decimal digits, a whole number divisor)
- Like above, but missing dividend or divisor
- Divide decimals by decimals (Think of how many times the divisor fits into the quotient.)
- Mixed multiplication and division problems 1 (1 decimal digit)
- Divide whole numbers and decimals by 10, 100, or 1000
- Same as above, missing dividend or divisor
- Multiply or divide decimals & whole numbers by 10, 100, and 1000
- Divide whole numbers and decimals by 10, 100, 1000, or 10,000
- Divide whole numbers and decimals by 10, 100, 1000, or 10,000 - missing dividend or divisor
Convert measuring units using long division & multiplication (paper & pencil) or mental math
- Convert between inches & feet
- Convert between inches, feet, and yards
- Convert between ounces & pounds
- Convert between tons & pounds
- Convert between cups, pints, and quarts
- Convert between cups, pints, quarts, and gallons
- Convert between ounces, cups, and quarts
- All customary units except miles - mixed practice
- All customary units except miles - mixed practice - a challenge
Convert using a calculator, with decimals
- Convert between mm, cm and m - using decimals
- Convert between mm, cm, m, and km - using decimals
- Convert between ml & l and g & kg - using decimals
- All metric units mentioned above - mixed practice - using decimals
- Metric system: convert between the units of length (mm, cm, dm, m, dam, hm, km)
- Metric system: convert between the units of weight (mg, cg, dg, g, dag, hg, kg)
- Metric system: convert between the units of volume (ml, cl, dl, L, dal, hl, kl)
- Metric system: convert between the units of length, weight, and volume
Prime factorization, GCF, and LCM
Fraction addition and subtraction
In all fraction multiplication and division problems, it helps to simplify before you multiply.
Convert fractions to mixed numbers and vv
Simplify or equivalent fractions
Fractions vs. Decimals
Addition & subtraction
Addition and subtraction of integers are beyond the Common Core Standards for grade 6 but some curricula or standards may include them in 6th grade.
Multiplication & Division
Multiplication and division of integers are beyond the Common Core Standards for grade 6 but the worksheets links are included here for completeness sake, as some curricula or standards may include them in 6th grade.
Area - these worksheets are done in the coordinate grid.
Volume & surface area
Since these worksheets below contain images of variable sizes, please first check how the worksheet looks like in print preview before printing. If it doesn't fit, you can either print it scaled (such as at 90%), or make another one by refreshing the worksheet page (F5) until you get one that fits.
If you wish to have more control on the options such as number of problems or font size or spacing of problems, or range of numbers, just click on these links to use the worksheet generators yourself: